Method and System for Communicating Multimedia Using Reconfigurable Rateless Codes and Decoding In-Process Status Feedback

ABSTRACT

A method and system use capacity-approaching rateless code to communicate multimedia data even with very short codewords, such as 64 bits or less, via erasure and noise channels. The method provides a way to design the edge degree distribution of rateless codes for any arbitrary channel. Based on an equivalent metric of decoding behavior in any channels, the degree distribution of a rateless code such as Luby-transform codes and raptor codes is optimized based on in-process status of decoding. A regularized least-squares optimization is used to avoid erroneous decoding. Multiple feedbacks can further improve the performance.

FIELD OF THE INVENTION

This invention relates generally to digital communications, and moreparticularly to communicating multimedia using rateless codes andfeedback.

BACKGROUND OF THE INVENTION

Realizing reliable communications is an important problem inpacket-based communication networks using packet erasure channels, wherepackets are either received and decoded, or lost. This channel model isrelated to a binary erasure channel (BEC). If a feedback channel isavailable, the channel capacity can be achieved with an automaticrepeat-request (ARQ). The receiver feeds back an acknowledgment for eachdecoded packet, and unacknowledged packets are retransmitted. BecauseARQ uses frequent feedback, ARQ is difficult to implement in manypractical networks, and increases overhead.

Rateless coding can achieve reliable communications on erasure channelswithout frequent feedback. Practical rateless codes include fountain,raptor, tornado, and Luby-transformation (LT) codes. Rateless codes canapproach the channel capacity in erasure channels if the code length issufficiently long. The rateless codes generate a potentially infinitenumber of encoded symbols from input symbols to approach the channelcapacity. Transmission of the encoded symbols is terminated when allsymbols have been correctly decoded.

FIG. 1 shows conventional rateless encoding 100 at a transmitter.Generally, the encoding uses high-rate outer block encoding. Randomparity of the data is transmitted until the encoded parity issuccessfully decoded.

A sequence of symbols (codeword) 101 is encoded by an outer block errorcorrection encoder 102, such as low-density parity-check (LDPC) codes.The encoded bits 103, referred to as input symbols, are fed to, e.g.,the LT encoder 110. The encoder is shown as a Tanner graph.

The input symbols are combined by an exclusive-or (XOR) operation toproduce the encoded output symbols. Each output symbol is the XOR'edparity bit by combining the random input symbols. The number of edges105 from the input symbols used in the XOR is referred to as a degree106 of the output symbol, and all input symbols contained in an outputsymbol are called neighbors of the output symbol. The edges are selectedat random according to the degree distribution. This process can beiterated to transmit 107 until the input symbols are decoded from thereceived output symbols.

FIG. 2 shows a conventional decoder 200 for a receiver of rateless codesthat uses belief propagation (BP). A general decoding process ofrateless codes includes determining the likelihood of reception,propagating belief information via edges, and correcting errors by outererror correction decoding. The BP decoding 201 is simple for erasurechannels if every symbol is error-free and can be decoded.

All degree-1 output symbols 203 are identified and moved to a storagereferred to as a ripple 204. The ripple has an associated size. Degree-1output symbols are symbols that have a single neighbor input symbol.Symbols in the ripple are processed by the XOR operation of the ripplenode to the neighbors. After a symbol has been processed 205, the symbolis removed from the ripple and considered decoded. The processing ofsymbols in the ripple potentially reduces some of the buffered symbolsto degree one, in which case they are moved to the ripple. This iscalled a symbol released.

The iterative decoding process 201 can be summarized as follows.Identify all degree-one symbols and add the symbols to the ripple.Process a symbol from the ripple, and then remove the symbol. Afterprocessing, add new degree-1 symbols to the ripple. This iterationcontinues while there still is a symbol in the ripple. Decoding succeedswhen all input symbols are decoded. If the ripple size becomes zerobefore processing all input symbols, decoding has failed.

To design rateless codes, the ripple size parameter is an importantfactor in erasure channels. The performance depends significantly on howthis parameter evolves during decoding, and thus conventional methodsfor rateless coding have mostly focused on the size of the ripple bydetermining a suitable ripple evolution and a degree distribution, whichachieves that desired ripple size evolution.

One ideal ripple evolutions uses only one symbol in the ripple over alldecoding processes. This ideal ripple provides the so-called idealsoliton distribution (ISD) for edge degree distribution. Although ISD isoptimal for infinite code lengths, ISD is suboptimal in practice withfinite code lengths because decoding failure frequently occurs. One ofmodifications is to consider a margin of ripple size to avoid decodingfailure. This idea provides a robust soliton distribution (RSD).

Another modification is based on a random walk model, which yields asquare-root ripple evolution. Although rateless codes were originallydeveloped for erasure channels, rateless codes can also be used foradditive white Gaussian noise (AWGN) channels.

Channel feedback facilitates the coding, i.e., encoding and decoding.Real-time oblivious erasure correction can utilize the feedback tosignal the number of input symbols that have been decoded. With thisinformation, the transmitter selects a fixed degree for future encodedsymbols, which maximizes the probability of decoding new input symbols.

In conventional doped fountain coding, the receiver feeds backinformation on undecoded symbols. By sending undecoded symbols withhigher priority, that method improves the coding efficiency.

However, the decoding reliability and coding efficiency are suboptimalfor a short codeword with rateless coding. Those design techniques arenot compatible in practical feedback systems to obtain some feedbackfrom the decoder in noisy channel environments.

SUMMARY OF THE INVENTION

The embodiments of the invention provide a method for reliablemultimedia communications with feedback, wherein the communications arefrom a transmitter to a receiver. The feedback provides information tothe transmitter while data are transmitted, received and decoded. Forexample, the feedback includes in-process status of a rateless decoderat the receiver.

The method uses capacity-approaching rateless codes, even with veryshort codewords, e.g. 64 bits or less, while the conventional capacityapproaching codes based on low-density parity-check (LDPC) require morethan 10,000 bits. The method offers a way to design relates codes in anyarbitrary channel including additive white Gaussian noise (AWGN)channels, and a binary symmetric channel (BSC), as well as a binaryerasure channel (BEC).

The embodiments are a generalized design method stemming from theerasure channel. Based on an equivalent metric of decoding behavior inany channels, the degree distribution of the rateless code can beoptimized dynamically.

A regularized least-squares optimization is used to avoid erroneousdecoding. One embodiment of the invention enables multiple feedbackopportunities to further improve the performance.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of conventional encoding with rateless codes;

FIG. 2 is a schematic of conventional decoding with rateless codes;

FIG. 3 is a schematic of reconfigurable rateless coding incorporatinginformative feedback according to embodiments of the invention;

FIG. 4 is a graph of ripple size to evolve in a decoding process withfeedback information according to embodiments of the invention;

FIG. 5 is a block diagram of designing degree distribution to achievethe ripple evolution by using a least-squares optimization according toembodiments of the invention;

FIG. 6 is graph of the impact of feedback timing according toembodiments of the invention;

FIG. 7 is a graph ripple evolutions via least-squares optimization forsingle and double feedback opportunities according to embodiments of theinvention; and

FIG. 8 is a block diagram of a method for designing the degreedistribution based on ripple evolution in noisy channels according toembodiments of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The embodiments of the invention provide a method for reliablemultimedia communications with feedback, wherein the data arecommunicated from a transmitter to a receiver. The receiver feeds backinformation regarding the decoding process to the transmitter, so thatthe transmitter can optimize a degree distribution used by an encoder.The degree distribution is time-varying. The feedback is generated asthe decoding progresses. The feedback includes in-process status of therateless decoder at the receiver.

The rateless codes use feedback when it is available. For simplicity, wefocus on a single feedback. However, the concept of our rateless codingincorporating feedback can be generalized to any amount of feedback forerasure or noisy channel environments.

FIG. 3 shows a communication network 300, which uses reconfigurablerateless coding with feedback 308 according to embodiments of theinvention.

A transmitter 301 communicates with a receiver 302 via a channel 303,which can be subject to erasures and/or noise. Multimedia data 304 aretransmitted using a rateless encoder 305, which uses a degreedistribution 306. For example, the encoder 305 is an LT encoder.

The receiver 302 decodes the channel output signals using a beliefpropagation (BP) rateless decoder 307. The invention provides a way tooptimize 309 the reliability and efficiency of the rateless codes byusing the feedback 308, which contains in-process status of the ratelessBP decoder 307.

Using the feedback, the transmitter optimizes 309 the degreedistribution 306 for the rateless codes to improve the decodingefficiency.

With the erasure channel 303, the feedback 308 signals the transmitterwhich input symbols have been decoded at an optimal feedback timing.Hence, the transmitter knows exactly the symbols that have been decoded.

This enables the rateless LT encoder 305 to adapt the degreedistribution 306 dynamically. The encoder 305 excludes all decodedsymbols from future encoding to reduce overhead, and modifies the degreedistribution to ensure that the ripple size at the decoder does rapidlydecrease to zero without a decoding failure.

The determining of the ripple evolutions includes both the ISD and RSD.An improved ripple evolution is based on a random walk model, whichprovides a square-root ripple evolution.

As shown in FIG. 4, when there are feedback opportunities, thesquare-root ripple evolution is modified to a piece-wise square-rootevolution. This figure shows a determining ripple size evolution 401over a decoding process. A message (codeword) length is k bits, and anumber of decoded bits in process is L.

One design principle is to have a large enough margin for avoidingdecoding failures, yet small enough to avoid redundancy to decode allbits. Hence, the initial ripple size 402 is large enough, e.g. 10, whilethe last ripple 403 is zero. The ripple curve is defined as a piece-wisesquare-root function 404 over the decoding process as:

R(L)=c ₁√{square root over (L−(1−f ₁)k)} for L>(1−f ₁)k

R(L)=c _(i)√{square root over (L−(1−f _(i))k)} for (1−f _(i-1))k>L>(1−f_(i))k,

where R(L) is the ripple size, f_(i) is a fraction of the decodingprocess at the i-th feedback timing, and c_(i) is an appropriateconstant. At the feedback timing 405, where f₁k symbols are decoded, theripple size is near zero, i.e., 1.

FIG. 5 shows our method 500 for designing the degree distribution toachieve the determining ripple evolution for any code lengths. Twodifferent degree distributions are determined, for a single feedback,one before the feedback, and the other after the feedback.

The determining ripple size evolution R(L) 501 is mapped 502 to Q(L),which denotes an expected number of releases at the decoding step. Themapping is expressed as

${Q(L)} = {{\frac{L\left( {{R(L)} - {R\left( {L + 1} \right)} + 1} \right)}{L - \left( {{R\left( {L + 1} \right)} - 1} \right)}\mspace{14mu} {for}\mspace{14mu} k} > L \geq 0}$

where Q(k)=R(k).

The expected number of releases Q(L) is expressed by a theoreticalrelease probability q(d, L k) 503 of the degree d

${q\left( {d,L} \right)} = \frac{{d\left( {d - 1} \right)}L{\prod\limits_{j = 0}^{d - 3}\; \left( {k - \left( {L + 1} \right) - j} \right)}}{\prod\limits_{j = 0}^{d - 1}\; \left( {k - j} \right)}$as${{Q(L)} = {\sum\limits_{d = 1}^{k - L + 1}{n\; {\Omega (d)}{q\left( {d,L,k} \right)}}}},$

where n is the number of received symbols and Ω(d) is the degreedistribution. That is, Ω(d) represents a probability that an outputsymbol has degree d, (d=1, 2, 3, . . . ). For the case of singlefeedback, the method solves 505 the optimal degree distributions, i.e.,Ω₁(d) before feedback, and Ω₂(d) after feedback. Because the aboveequation is numerically unstable to solve, the invention uses aleast-squares optimization to obtain near optimal degree distributions.

FIG. 6 shows the efficiency in the sense of overhead of the LT codingwith single feedback as a function of the feedback timing f₁. Theoptimal feedback timing is about f₁=0.75 for piece-wise square-rootripple evolutions. The curves, from top to bottom are for k=128, 256,512, 1024, and 2048. The graph shows that shorter codes need moreoverheads, and the method using feedback can significantly reduces theoverhead.

The design method, which uses the least-squares optimization andpiece-wise square-root ripple evolution, can be extended to the case ofmultiple intermediate feedback opportunities. The number of feedbackopportunities can be a network parameter. The least-squares solutionachieves optimal determining ripple evolutions.

FIG. 7 shows an example of achieved near optimal ripple evolutions toapproach the determining piece-wise square-root ripple for the similarcases of single and double feedback cases.

The conventional RSD has a considerably large overhead, while our LTcoding with feedback can significantly improve the efficiency of thecoding. The invention also decreases the encoding/decoding complexitybecause the average degree is decreased.

The rateless raptor coding structure, which uses an outererror-correction code, can further reduce the coding (encoding/decoding)complexity.

xxThe invention can be applied to the raptor coding by adding aconstraint of the average degree into the least-squares optimization.The average degree is expressed as

$\overset{\_}{d} = {\sum\limits_{i = 1}^{m + 1}{\frac{n_{i}}{n}{\sum\limits_{d = 1}^{k_{i - 1}^{\prime} - k_{i}^{\prime}}{d\; {\Omega_{i}(d)}}}}}$${n = {\sum\limits_{i = 1}^{m + 1}n_{i}}},$

where m is the number of feedback opportunities, k′_(i)=(1−f_(i))k withf_(i) is the i-th feedback timing, n_(i) is the received symbol at thei-th feedback. This equation is added to the least squares optimizationwith a relatively large constraint weighting.

The ripple size is near zero at the feedback timing for piece-wisesquare-root evolutions. If it becomes exactly zero, then the decodinghas failed. To avoid such a decoding failure, a constraint is added tothe least-squares optimization so that the sufficient amount of releasesis achieved prior to the feedback. And, the feedback is performed whenthe actual ripple size becomes 1 to avoid decoding failure.

For raptor coding of k=128 bits with single feedback, the average degreeis reduced to be half of the comparable LT code, and hence, thecomplexity is half.

FIG. 8 shows an embodiment of the invention for degree optimization innoisy channels, instead of erasure channels based on ripple analysis.For noisy channels, the BP decoding becomes more complicated because thechannel output is not perfectly reliable. While the conventional BPdecoding uses a batch scheduling, in which a belief message issimultaneously propagated, it is known that sequential scheduling suchas random propagation performs better.

The feedback information for noisy channels includes belief messages.The belief propagation messages indicate the reliability of the decodingof each symbol. Using this information, the transmitter optimizes thedegree distribution and priority weighting according to the reliability.

The embodiment first analyzes the entropy of the belief messages 802,for such a modified scheduling 801. Based on the entropy, the inventionprovides a way of equivalently interpreting the noisy channels into theerasure channels by determining 803 the information-theoretic mutualinformation 804, which defines an equivalent ripple. The mutualinformation is then used to optimize the degree distribution using theleast-squares optimization 805.

For noisy channels, the optimal degree distribution depends on the errorprobability or the noise variance. To deal with the impact of the noisevariance, the embodiment of the invention uses a modified random walkmodel 806 to optimize the determining ripple. Because the belief messagemay contain erroneous information, the least-squares optimization isalso modified to improve the performance by adding a regulation term toavoid trapping 807 during erroneous belief propagation 807. With updateddegree distribution, the optimization process from the entropy analysis802 to the degree design 805 iterates 808 until convergence.

A conventional random walk model assumes increment or decrement atrandom for one symbol decoding process. For noisy channels, theprocessed symbol is not always one symbol. The embodiment uses ahigh-order polynomial to model the transient movement. For most cases,the first-order polynomial has a sufficiently good performance. Withthis modified random walk model, the determining ripple evolution isexpressed by a bended square-root function.

For noisy channels, the BP decoding can be trapped by an even number oferroneous belief messages in neighbors. Such a trapping can be avoidedby maximizing the probability of an even number of error bits comparedto the probability of an odd number of error bits. The regularizedleast-squares optimization maximizes this probability subject to squarederror of the ripple equation.

Another embodiment of the invention, the outer block error-correctingcode is at a relatively high rate, i.e., greater than 0.95, and includesnonlinear block coding linear block coding so that layered multimediadata have unequal error protection for layered multimedia data by usingnonlinear block error correction codes, rather than linear block coding.A random edge selection is modified by considering priority information,which is obtained from the feedback.

While the degree distribution can be designed off-line, an informativefeedback can reconfigure the degree distribution and priority weightingdynamically in real-time-line.

The embodiments provide a way to reconfigure those parameters byMonte-Carlo simulation of an expected performance before transmitting.After Monte-Carlo simulations, the optimal performing degreedistribution is selected.

Although the invention has been described by way of examples ofpreferred embodiments, it is to be understood that various otheradaptations and modifications can be made within the spirit and scope ofthe invention. Therefore, it is the object of the appended claims tocover all such variations and modifications as come within the truespirit and scope of the invention.

We claim:
 1. A method communicating multimedia information from atransmitter to a receiver, comprising the steps: encoding, in thetransmitter, the multimedia data by a rateless encoder to produceencoded data, wherein the rateless encoder uses a time varying degreedistribution; transmitting the encoded data to the receiver via achannel; decoding, in the receiver, an output of the channel by adecoder; transmitting, from the receiver to the transmitter, feedback ofan in-process decoding status of a rateless decoder at the receiver atan optimal feedback timing while receiving the encoded data; andoptimizing dynamically, in the transmitter, the degree distributionbased on the feedback.
 2. The method of claim of 1, wherein the degreedistribution is optimized by performing the steps: using a determiningripple evolution; mapping the determining ripple evolution to a releaseevolution; and applying least-squares optimization to a ripple equationsbased on a theoretical release probability.
 3. The method of claim of 1,wherein the channel is subject to noise, and further comprising thesteps: modifying a belief propagation scheduling of a belief propagationdecoder from a batch update to a sequential random update; analyzing anentropy of belief messages; determining mutual information to obtain anequivalent ripple size for the channel; optimizing the degreedistribution using a regularized least-squares optimization, wherein theregularized least squares optimization incorporates a modified randomwalk model and trapping avoidance; and iterating until the degreedistribution convergences to the optimal degree distribution.
 4. Themethod of claim of 3, wherein the ripple size is designed by themodified random walk model, and wherein the random walk model uses ahigh-order polynomial movement, resulting into a piece-wise square-rootripple for an erasure channel, and a bended square-root ripple for thenoisy channels.
 5. The method of claim of 3, wherein the encoded dataincludes input symbols and output symbol, and further comprising:performing trapping avoidance by determining a failure probability of aneven number of error messages, and a successful probability of an oddnumber of error messages contained in neighbors, wherein all inputsymbols contained in a particular output symbol are the neighbors of theoutput symbol.
 6. The method of claim of 1, wherein optimal feedbacktiming for multiple feedbacks is optimized by evaluating an expectedoverhead.
 7. The method of claim of 1, wherein the feedback is done whenthe actual ripple size became 1 and an expected release is added in theconstraint term of a least-squares optimization to avoid decodingfailure at those timing.
 8. The method of claim of 1, wherein a randomedge selection is modified to a non-uniform random edge selection toconsider priority information in the feedback.
 9. The method of claim of1, wherein an outer block error-correcting code uses a rate greater than0.95, and includes nonlinear block coding and linear block coding sothat layered multimedia data have unequal error protection capability.10. The method of claim of 1, wherein a number of feedback opportunitiesis selected as a network parameter.
 11. The method of claim of 1,wherein the degree distribution is optimized off-line.
 12. The method ofclaim of 1, wherein the degree distribution is optimized on-line usingMonte-Carlo simulations.
 13. The method of claim 1, wherein the feedbackincludes belief propagation messages of in-process decoding at thereceiver.
 14. The method of claim 1, wherein at the optimal timing aripple size of the decoder is
 1. 15. The method of claim 14, wherein thedecoding reduces the size of the ripple according to a piece-wisesquare-root function.
 16. The method of claim 14, wherein an initialsize of the ripple is
 10. 17. The method of claim 1, wherein the ripplesize is a piece-wise square-root, where the feedback timing is afraction 0.75 of the decoding process for a single feedback case. 18.The method of claim 1, wherein a size of a codeword used by the 0.2encoding and decoding is 64 bits or less.
 19. The method of claim 1,wherein the decoder is a-rateless belief propagation decoder.
 20. Anetwork for communicating multimedia with informative feedback,comprising: a transmitter configured to encode the multimedia data by arateless encoder to produce encoded data, wherein the rateless encoderuses a time varying degree distribution; and a receiver configured todecode the encoded data received via a channel from the transmitterusing a decoder, wherein the transmitter feeds back a decoding status atan optimal feedback timing while receiving the encoded data to enablethe transmitter to optimize dynamically the degree distribution based onthe feedback.